Geometry apparatus

ABSTRACT

Apparatus for mathematical-geometric experimentation with variable straight lines, distances, angles, and areas in one plane.

United States Patent [191 Schulte et a].

[ GEOMETRY APPARATUS [76] Inventors: Erich Schulte, I-lagener Str. 25,

Nachrodt; Ulrich Hebel, Helenenweg 7, Kirchen, both of Germany [22] Filed: May 1, 1972 [211 App]. No.: 249,028

[30] Foreign Application Priority Data May 3, 1971 Germany G 71 16 996.5 June 21, 1971 Germany G 71 27 928.6

[52] US. Cl. 133/76 R, 33/86, 33/1 K [51] Int. Cl B431 5/02, B431 13/14 [58] Field of Search35/34; 33/77, 76, 85, 86, 184.5,

[56] References Cited UNITED STATES PATENTS 2,507,460 5/1950 Schacht 35/34 Jan. 22, 1974 2,446,253 8/1948 Tresidder 33/86 633,263 9/1899 Grant.... 33/86 1,072,908 9/1913 Buda 33/86 2,585,160 2/1952 Munn 33/85 2,529,413 11/1950 Petersen 33/1 B FOREIGN PATENTS OR APPLICATIONS 145,175 4/1931 Switzerland 33/77 418,959 10/1956 Germany 333/76 R 1,102,610 3/1961 Germany 33/76 R [57] ABSTRACT Apparatus for mathematical-geometric experimentation with variable straight lines, distances, angles, and areas in one plane.

11 Claims, 10 Drawing Figures l l\lllllllll I II PATENTEUJANZ 2M SHEET 3 OF 3 GEOMETRY APPARATUS BACKGROUND OF THE INVENTION At the present time, mathematic-geometric problems have been shown in diagrams and drawings by putting down on paper lines of different shape with the help of straight edges, triangles and drawing pencils. It was of advantage to use drawing templates. In educational training (particularly because of the necessary changes in the drawings on the way to the final solution) valuable time was lost; considerable paper was required and the students material requirements were greater than necessary. These and other difficulties experienced with the prior art devices have been obviated in a novel manner by the present invention.

It is, therefore, an outstanding object of the invention to provide an apparatus making it possible to make first the mathematic-geometric experiment without drafting work and then, if necessary, to put on paper the solution found.

Another object of this invention is the provision of apparatus making it possible to vary all variables present in one problem in an infinitely variable manner and to show all functional connections.

A further object of the present invention is the provision of apparatus permitting the user to solve geometrical problems and the like by the trial-and-errror method without considerable work and the use of large amounts of paper.

With these and other objects in view, as will be apparent to those skilled in the art, the invention resides in the combination of parts set forth in the specification and. covered by the claims appended hereto.

SUMMARY OF THE INVENTION In general, the accomplishment of this task, according to technique and procedure of this invention, is brought about mainly by showing mathematical terms like straight lines by the use of threads. A thread is positioned between two end points, located outside the working area, and the end points of all straight lines, for the determination of their position within the working area independent of each other, run along tracks positioned out of the working area and may be displaced and secured into any position. v

More specifically, distances, angles and areas can be defined by several threads crossing each other and their positions may be determined by the adjustment of the ends of the threads. An especially secure and practical workmanship may be achieved by the use of elastic threads.

The apparatus for the execution of this procedure is mainly distinguished by a plate with a totally-enclosed, flat work area. Guide tracks are positioned outside the work area. These guide tracks are run parallel or perpendicular to each other. Also, the guide tracks could be of circularor bow-shaped configuration and equipped with any number of riders sliding in the guide tracks on different sides of the work area, thus forming anchor points for one or more stretched threads.

By arranging these threads on the plane and manipulating them, mechanical models are created, where the structure is isomorph to mathematical conception. Some of these conceptions (such as the representation of shear or stress) the student may only grasp correctly and clearly through such a device. The kinematic observation makes this apparatus similar to the edcuational movie and so increases the constructive thinking of the student.

In accordance with a modification of this invention, the threads are made from elastic material, such as thin, round rubber threads.

The guide tracks of the plate are preferably formed, according to this invention, by bars running along the plate edge, by grooves, or by notches; the riders have supports fitting the shape of the guide tracks.

The guide tracks may also be formed by a permanent magnet or consist of magnetizable bars or strips, the riders having supports of permanent magnets or magnetizable material.

According to this invention, the riders along the guide tracks may be purposely made so that they are difficult to move and, for example, may fit with a clamping seat on the bars or in the grooves or notches.

According to this invention, it is also possible that the riders located on the side areas opposing each other are equipped with a plurality of grooves for guiding the threads and also are equipped with a hole in their center. One end of the thread is placed in the hole and maintained there by a knot. The thread may then, starting from the hole, be positioned selectively into one or the other of the guide grooves.

So that the elastic threads are always positioned close to the working area during experimentation, the guide grooves within the side areas of the riders are (at least on the side facing the working area) at the same elevation as the plane of the working area.

It was found to be especially of advantage to design the riders with a base body and a cap which may be interlocked with the body; between these two parts are clamped one or more thread ends.

For an improved experimentation, provision is made for two or more thread ends to be clamped on one rider; this requires repeated removal and replacement of the cap. Therefore, the base body and the cap of the rider, for practical purposes, consist of an elastic and wear-resistable material, such as polyamide.

In case the experimental solution, found with the help of the threads, has to be put down on paper, a paper clamping device or a drafting machine is arranged or mounted at the side of the working area.

BRIEF DESCRIPTION OF THE DRAWINGS The character of the invention, however, may be best understood by reference to one of its structural forms, as illustrated by the accompanying drawings, in which:

FIG. 1 is a plan view of apparatus constructed in accordance with the principles of this invention, showing a drawing sheet, equipped with pre-printed divisions and scales over which threads are stretched for the demonstration of mathematic-geometric problems,

FIG. 2 shows in an enlarged scale, a cross-section through the edge of the apparatus and the rider connected to it,

FIG. 3 shows a section of a modified form of the apparatus,

FIG. 4 is a further enlarged longitudinal section of the rider shown in FIG. 2,

FIG. 5 shows the rider of FIG. 2 in side view,

FIG. 6 is a plan view of the rider shown in FIG. 4 and FIG. 7 is a sectional view taken on the line A-A in FIG. 4,

FIG. 8 shows a side view of another design of a rider,

FIG. 9 is a longitudinal section view of the rider according to FIG. 8, and

FIG. 10 is a cross-sectional view of the same rider.

DESCRIPTION OF THE PREFERRED EMBODIMENT In FIG. 1 it can be seen that the geometric apparatus of the invention shows a plate 1 on which is positioned a paper sheet having divisions printed in millimeters and a circular section system, the sheet being kept in place by a paper clamping bar 2. Over the working area are stretched threads 3 made of strong, elastic, round rubber, their ends being corrected to riders 4. These riders 4 are movable mounted on bars 6 formed on the plate 1, the bars forming guide tracks for the riders and extending along the plate edges lain parallel or at right angles to each other. The pattern pictured on the sheet of paper stretched over the plate 1 is an example of a graphic solution of an equation.

FIG. 2 shows the shape in profile of the riders 4 and the bars 6 which are arranged along the edges of the base plate I for support and guidance.

Another profile shape of a rider 34 and the corresponding edge formation 35 and 36 of a plate 31 is shown in FIG. 3.

According to FIG. 2, a groove 5 is formed in the upper side of the plate 1 in such a way that a bar 6 of a rectangular cross-section is formed on the upper side of the plate. The dimensions of the fitted profiled riders 4 are of such a kind that they may be lightly clamped within the grooves 5 and the bars 6. The clamping action is assisted by tension in the threads 3.

According to FIG. 3, the groove 5a is cut into the underside of the plate la from the edge, so that a laterallyextending bar 60 is formed holding the rider 4a.

The design of the riders 4 is shown in detail in FIGS. 4 to 7. Each rider made in such a way that is has open guide grooves 4b on both sides for threads 3. The threads 3 have their ends pushed through the hole 4a and fastened by means of a knot 30 underneath. The two side guide grooves 4b meet in the area of the penetrating hole on the upper side of rider 4, so that the thread 3 may be positioned into one or the other of the side guide grooves 4b. The front end of the side guide groove 4b is located at the same height as the working area of the plate 1, so that the threads are placed close to the working area when the riders with their base parts are engaged with the grooves 5 or bars 6.

The design of a rider 14 shown in FIGS. 8 to 10 differs mainly from the ones shown in FIGS. 2 to 7 in that it has a base part 15 and a cap 16 interengaged with each other. Between these two parts is inserted the end of the thread 3 (before they are engaged with one another), so that the threads are clamped tightly after such engagement. Several thread ends can be clamped on one rider at the same time.

For the purpose of interengagement, the base part of the rider has side grooves 17 with which mating parts 18 (arranged at the inside of the cap) are engaging. The base part 15 and the cap 16 of the rider 14 are preferably formed of elastic and wear-resistant material, such as polyamide.

The base part 15 of the rider 14 is provided with such a conformation that it engages one side of the groove 5 at the upper side of the plate 1 and also surrounds the bar 6 with a clamping force. It has been found to be practical to equip the base part 15 (which engages the groove 5 on the upper side of the the plate 1) with an inside curvature 19 with which it comes into clamping contact during engagement with the bar 6 at its inside. A slot 20 arranged at the side within cap 16 serves as a centering notch for the clamped rubber thread, which has it end clamped between the cap 16 and the base part 15. Side ribs 21 on the cap 16 increase the grip of the rider 14 during operation.

The plate can be made out of opaque materials for the student. For the teacher however, the plates may be made from transarent or from light-penetrating materials, so that they may be used, if necessary, in connection with a projector if the execution of a mathermaticgeometric experiment is to be shown to a number of pupils for follow-up of the experiment.

In the operation of the apparatus, the rider 4 may be displaced selectively along the bars 6 and grooves 5 (designed as guide tracks) and, when required, may be displaced to any chosen guide track where they clamp themselves tightly in any desired position. With the help of the threads 3 stretched between the riders four lines are created which run horizontally, vertically and with any slope. By the use of several threads 3 at the same time variable slopes, lines, angle and areas may be formed over the work area on the plate.

After the solution of any provelm has been found, it is still possible to draw problem solution as shown by the threads onto a worksheet clamped to the plate 1.

There are many uses for the mathematic experimental plate and it could be used, for example, to solve algebraic and geometric tasks by experiment and, thereafter, to show them on a drawing.

It is obvious that minor changes may be made in the form and construction of the invention without departing from the material spirit thereof. It is not, however, desired to confine the invention to the exact form herein shown and described, but it is desired to include all such as properly come within the scope claimed.

The invention having been thus described, what is claimed as new and desired to secure by Letters Patent 1. Apparatus for mathematic-geometric experimentation with variable straight lines, distances, angles, and areas in one plane, comprising a. a flat plate having opposed peripheral edges and a flat working area on an upper surface,

b. a clamp capable of holding a sheet of paper on the upper surface of the plate,

0. a first and a second rider movable along opposed edges of the plate, and

d. an elastic thread which is connected to each of the riders and extends from it at a point on the riders adjacent the upper surface of the plate,

the riders being equipped with grooves on opposing side surfaces for guiding the thread and having within the longitudinal plane a penetrating hole in which the end of the thread may be fastened by knotting, the thread from the penetrating hole being selectively positioned in one of the guide grooves.

2. Apparatus as recited in claim 1, wherein the guide grooves on the side surfaces of the riders are at the end facing the working area at the same elevation as the working area.

3. Apparatus as recited in claim 1, wherein the plate with the flat working area is defined on all sides by straight guide tracks arranged outside the working area and running either parallel to each other or at a right angle, the tracks being equipped with a plurality of riders capable of being placed on the guide tracks, the riders being displacable along these tracks to form arresting points for threads at different sides of the working area.

4. Apparatus as recited in claim 1, wherein the threads are made from elastic material in the form of thin round rubber.

5. Apparatus as recited in claim 3, wherein the guide tracks of the plate are formed as bars, grooves, and notches along the edges of the plate and the riders have base parts fitted to the shape of the guide tracks.

6. Apparatus as recited in claim 3, wherein the guide tracks of the plate are magnetic elements and the riders have magnetic base parts.

7. Apparatus as recited in claim 5, wherein the riders slide with difficulty within the guide tracks and are fitted with clamping seats to the bars and grooves.

8. Apparatus as recited in claim 1, wherein the clamp is a paper-clamping bar and is located at one side of the working area.

9. Apparatus as recited in claim 1, wherein the working area defines a portion of the plate that is transparent.

10. Apparatus for mathematic-geometric experimentation with variable straight lines, distances, angles, and areas in one plane, comprising a. a flat plate having opposed peripheral edges and a flat working area on an upper surface,

b. a clamp capable of holding a sheet of paper on the upper surface of the plate,

c. a first and second rider movable along opposed edges of the plate, the riders consisting of a base body and an interlocking cap and between these two parts at least one threaded end which the body and cap may be tightly clamped together, and

d. an elastic thread which is connected to each of the riders and extends from it at a point on the riders adjacent the upper surface of the plate.

11. Apparatus as recited in claim 10, wherein the base body and the cap consist of elastic and wearresistant material. 

1. Apparatus for mathematic-geometric experimentation with variable straight lines, distances, angles, and areas in one plane, comprising a. a flat plate having opposed peripheral edges and a flat working area on an upper surface, b. a clamp capable of holding a sheet of paper on the upper surface of the plate, c. a first and a second rider movable along opposed edges of the plate, and d. an elastic thread which is connected to each of the riders and extends from it at a point on the riders adjacent the upper surface of the plate, the riders being equipped with grooves on opposing side surfaces for guiding the thread and having within the longitudinal plane a penetrating hole in which the end of the thread may be fastened by knotting, the thread from the penetrating hole being selectively positioned in one of the guide grooves.
 2. Apparatus as recited in claim 1, wherein the guide grooves on the side surfaces of the riders are at the end facing the working area at the same elevation as the working area.
 3. Apparatus as recited in claim 1, wherein the plate with the flat working area is defined on all sides by straight guide tracks arranged outside the working area and running either parallel to each other or at a right angle, the tracks being equipped with a plurality of riders capable of being placed on the guide tracks, the riders being displacable along these tracks to form arresting points for threads at different sides of the working area.
 4. Apparatus as recited in claim 1, wherein the threads are made from elastic material in the form of thin round rubber.
 5. Apparatus as recited in claim 3, wherein the guide tracks of the plate are formed as bars, grooves, and notches along the edges of the plate and the riders have base parts fitted to the shape of the guide tracks.
 6. Apparatus as recited in claim 3, wherein the guide tracks of the plate are magnetic elements and the riders have magnetic base parts.
 7. Apparatus as recited in claim 5, wherein the riders slide with difficulty within the guide tracks and are fitted with clamping seats to the bars and grooves.
 8. Apparatus as recited in claim 1, wherein the clamp is a paper-clamping bar and is located at one side of the working area.
 9. Apparatus as recited in claim 1, wherein the working area defines a portion of the plate that is transparent.
 10. Apparatus for mathematic-geometric experimentation with variable straight lines, distances, angles, and areas in one plane, comprising a. a flat plate having oPposed peripheral edges and a flat working area on an upper surface, b. a clamp capable of holding a sheet of paper on the upper surface of the plate, c. a first and second rider movable along opposed edges of the plate, the riders consisting of a base body and an interlocking cap and between these two parts at least one threaded end which the body and cap may be tightly clamped together, and d. an elastic thread which is connected to each of the riders and extends from it at a point on the riders adjacent the upper surface of the plate.
 11. Apparatus as recited in claim 10, wherein the base body and the cap consist of elastic and wear-resistant material. 